Microsoft Compliance Manager (Preview) is a free workflow-based risk assessment tool that lets you track, assign, and verify regulatory compliance activities related to Microsoft cloud services. Azure Cloud Shell, on the other hand, is an interactive, authenticated, browser-accessible shell for managing Azure resources.
References:
https://docs.microsoft.com/en-us/microsoft-365/compliance/compliance-manager-overview
https://docs.microsoft.com/en-us/azure/cloud-shell/overview